Notes on AdS_3

Abstract

We use the conjectured strong-weak coupling worldsheet duality between the SL(2)/U(1) and Sine-Liouville conformal field theories to study some properties of degenerate operators and to compute correlation functions in CFT on AdS_3. The same quantities have been computed in the past by other means. The agreement between the different approaches provides new evidence for the duality. We also discuss the supersymmetric analog of this duality, the correspondence between SCFT on the cigar and N=2 Liouville. We show that in the spacetime CFT dual to string theory on AdS_3 via the AdS/CFT correspondence, the central term in the Virasoro algebra takes different values in different sectors of the theory. In a companion paper we use the results described here to study D-branes in AdS_3.

40 pages, harvmac; references added

References in corpus (2)

• Comments on the Thermodynamics of Little String Theory
• String Theory on AdS_3 and Symmetric Products

Cited by in corpus (69)

• Liouville Field Theory -- A decade after the revolution
• Strings in AdS_3 and the SL(2,R) WZW Model. Part 3: Correlation Functions
• Phases of Quantum Gravity in AdS3 and Linear Dilaton Backgrounds
• From Big Bang to Big Crunch and Beyond
• Holography Beyond AdS
• LSZ in LST
• A Solvable Irrelevant Deformation of $Ad{S}_3/CF{T}_2$
• String theory on ${\text{AdS}}_3$ and the symmetric orbifold of Liouville theory
• Strings on warped AdS${}_3$ via $T\bar{J}$ deformations
• Summing over Geometries in String Theory
• $T\bar{T}$-deformations, AdS/CFT and correlation functions
• D-branes in N=2 Liouville and its mirror
• BMS, String Theory, and Soft Theorems
• The Spectrum of Strings on Warped AdS_3 x S^3
• Little String Theory and Heterotic/Type II Duality
• String Theory of Supertubes
• Two-Point String Amplitudes
• Type 0 Strings in a 2-d Black Hole
• String theory at the tip of the cigar
• String dynamics in NS5-F1-P geometries
• On the Central Charge of Spacetime Current Algebras and Correlators in String Theory on AdS3
• On Solvable Time-Dependent Model and Rolling Closed String Tachyon
• Coulomb integrals for the SL(2,R) WZNW model
• The Cheshire Cap
• Heating up holography for single-trace $J\bar{T}$ deformations
• Stringy Black Hole Interiors
• Asymptotic Symmetries of String Theory on AdS3 X S3 with Ramond-Ramond Fluxes
• On the Boundary Dynamics of Chern-Simons Gravity
• More AdS_3 correlators
• Stringy ER=EPR
• Thermal AdS(3), BTZ and competing winding modes condensation
• Stringy Horizons and UV/IR Mixing
• On Spectral Flow Symmetry and Knizhnik-Zamolodchikov Equation
• Two-charge small black hole entropy: String-loops and multi-strings
• Holography and the Polyakov action
• Non-Supersymmetric Seiberg Duality, Orientifold QCD and Non-Critical Strings
• The String Theory on AdS_3 as a Marginal Deformation of a Linear Dilaton Background
• Worldsheet computation of heavy-light correlators
• The AdS3 central charge in string theory
• A Puncture in the Euclidean Black Hole
• Notes on the Verlinde formula in non-rational conformal field theories
• Remarks on free field realization of SL(2,R)/U(1) x U(1) WZNW model
• c < 1 String from Two Dimensional Black Holes
• Branes in the OSP(1|2) WZNW model
• Free field realization of superstring theory on AdS3
• FZZ Algebra
• FZZ Scattering
• A localising AdS${}_3$ sigma model
• Holographic Weyl anomaly in string theory
• Non-Critical String Duals of N=1 Quiver Theories
• Penrose limit and string quantization in AdS_3 \times S^3
• Heterotic warped Eguchi-Hanson spectra with five-branes and line bundles
• More on Long String Dynamics in Gravity on AdS3: Spinning Strings and Rotating BTZ
• A note on the spectral flow operator
• String correlators in AdS${}_3$ from FZZ duality
• The AdS3 boundary energy momentum tensor, exact in the string length over the curvature radius
• Zamolodchikov operator-valued relations for SL(2,R)_k WZNW model
• Asymptotic Symmetries in the TsT/$T\bar{T}$ Correspondence
• Solvable time-like cosets and holography beyond $AdS$
• Stringy horizons and generalized FZZ duality in perturbation theory
• Orientifolds in N=2 Liouville Theory and its Mirror
• A Note on Z_2 Symmetries of the KZ Equation
• On marginal deformation of WZNW model and PP-wave limit of deformed $Ad{S}_3\times S^3$ string geometry
• Asymptotically Free AdS3/CFT2
• SUSY Enhancements in (0,4) Deformations of AdS_3/CFT_2
• The infinite curvature limit of AdS/CFT
• Non-critical string, Liouville theory and geometric bootstrap hypothesis
• Lecture notes on strings in AdS${}_3$ from the worldsheet and the AdS${}_3$/CFT${}_2$ duality
• A Defect in AdS3/CFT2 Duality